Bolt falls off rocket, find rocket acceleration

In summary, a rocket with constant acceleration was launched straight up, and after 4 seconds a bolt fell off and hit the ground 6.70 seconds later. To find the rocket's acceleration, work backwards and use the equations h = 1/2 at^2 and v = at to find the height and speed of the rocket after 4 seconds. Then, use the equation h = h_0 + v_0t - (g/2)t^2 to find the height of the bolt after it leaves the rocket, setting h = 0 when t = 6.7 seconds and solving for a.
  • #1
stangeroo
13
0
A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 6.70 s later.

Find the rockets acceleration.

I don't understand how to set up this problem, I've never done something like this , asked some friends and they didnt know how to do it. Any help would be greatly appreciated :smile:
 
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  • #2
Work backwards kind of. If it took 6.7 for the bolt to hit the ground, how high was it?

[tex]d = v_{i}t + \frac{1}{2}at^2[/tex]

vi = 0
a = -32 ft\sec^2 or -9.8 m\sec^2
t = 6.7 s

Solve for d.

Now, use the same equation and solve for "a" of the rocket.

[tex]d = v_{i}t + \frac{1}{2}at^2[/tex]

d = part a
vi = 0
t = 4


Jameson
 
  • #3
Do it in two parts, but like this:
Part 1: Find the height and speed of the rocket after 4 seconds in terms of the rocket acceleration. Use:
[itex]h = 1/2 a t^2[/itex] and
[itex]v = a t[/itex]

Part 2: Realize that the initial height and speed of the bolt equals the height and speed of the rocket after 4 seconds (which was calculated in part 1). The height of the bolt after it leaves the rocket is:
[itex]h = h_0 + v_0t -(g/2)t^2[/itex],
using [itex]h_0[/itex] and [itex]v_0[/itex] (in terms of a) from part 1; set h = 0 when t = 6.7 seconds. Solve for a.
 
  • #4
thank you guys:cool:
 

1. How does the bolt falling off affect the rocket's acceleration?

When the bolt falls off the rocket, it decreases the rocket's acceleration. This is because the bolt was likely holding an important component in place that is now loose and may cause imbalance or drag on the rocket's movement.

2. Can the bolt falling off have any positive effects on the rocket's acceleration?

No, the bolt falling off will only have a negative effect on the rocket's acceleration. Without the bolt, the rocket's components may become loose and affect its trajectory or overall performance.

3. Is it possible to determine the acceleration of the rocket after the bolt falls off?

Yes, it is possible to determine the acceleration of the rocket after the bolt falls off. This can be done by analyzing the rocket's speed and position data before and after the bolt fell off, and using equations of motion to calculate the acceleration.

4. How can the bolt falling off be prevented in future rocket designs?

To prevent the bolt from falling off in future rocket designs, engineers can use stronger materials for the bolt, perform thorough testing and quality control measures, and ensure proper installation and maintenance procedures are followed.

5. Can the bolt falling off indicate any larger issues with the rocket's design?

Yes, the bolt falling off could indicate larger issues with the rocket's design. It could be a sign of weak or faulty components, inadequate testing, or inadequate maintenance procedures. It is important for engineers to investigate and address these issues to prevent future accidents and improve overall rocket performance.

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